I learned fast that when moving faster than most people on a bike, I need a bell. Some people dont want them on their bikes, mostly for aesthetic reasons. For me however, it is absolutely critical to let people know I am coming ahead of time. I feel uncomfortable shouting, and everyone recognizes the sound of a bicycle bell, which means they immediately respond appropriately rather than turn around and look.

I would not feel bad about it. Accidents happen, and it does not sound like it happened because you were irresponsible and took too many risks. Its just one of those things. Just be happy no one was really injured.